If it’s your neighbor’s chicken, they are free roaming, and come to your property then too bad for your neighbor’s loss. Had a similar situation with a neighbor’s chicken and my dog killed it after it came onto my property. I returned the remains to the neighbor, told him I was sorry about his loss, and suggested he may want to think about doing something to keep his chickens on his property to prevent future losses. (He and I got along good and he had no hard feelings because it was the chicken’s fault.)
Had similar issue here with three Great Pyrenees & Golden Lab mix dogs. We had them, they were born outside the house door. We live rural, in the county. There are no statutes, ordinances, laws that required us to either pen or tie out the dogs.
The county animal control officer even told us that herself. she had been called in by the county sheriff on behalf a newly moved in neighbor. This neighbor also let chickens roam free.
Our dogs roamed a bit but any time we stepped out, our dogs were near us. They slept where they had been born most nights. They would wander up to a sheep farm sometimes.
The sheep farm owner had no problems with our dogs, in fact wanted them coming up at night to help mitigate coyote. When our dogs brought me dead chickens, I tried taking the chicken carcass over to the new neighbor. Even offered to pay damages if asked and reasonable.
Each time I was brought a dead bird it never appeared that it was dead due to the dog. The dog had picked it and brought it to me as a gift, or "hey, what's going on". Each time I tried mending fence with this neighbor i got told all was fine, just go on.
So I stopped bothering fence mending. They kept letting chickens roam. We're all "out in the country" not only dogs go after chickens.
I did set up a building and fenced in area for the dogs. I tried keeping them "contained". These are big dogs though. They'll jump a 5/6 ft fence no problem. They'll dig under too.
They were also farm bred dogs. I didn't see why if they didn't bother sheep they would bother chickens. I got frustrated trying to contain them.
Suddenly we get two dogs taken away by animal control. Then just as sudden a hearing where it was "determined" I was abusing my dogs by way of "neglect". Anyone in the area by far knew damn sight better than suggest I "neglect" my dogs. It was obvious that was bull.
Wound up paying animal control X amount for feed and boarding, ordered to get rid of dogs. We took them to a no kill shelter to get adopted out. One went to Canada to be a hunting hound.
But yeah, ... um got a sour taste of a-holes.